The paper describes the first mathematical conceptual constructions of preschoolers and how they occur on working with children's stories. Current studies show how rich are those initial concepts; however, few among them take into account children's stories as a context for mathematical initiation. In order to evaluate the possibilities of that alternative, a group of seven children (five years-old) of a private preschool was composed at random in order to take three lessons about elementary arithmetical notions, presented as problems involving events of "Snow White and the seven dwarves". Orally presented by the researcher as a teacher, problems of the first and the second sessions referred to addition-subtraction, ratio two for one and comparison of intensive measures. On the third session, the children were invited to create problems about the story issues, but they also solved problems proposed by the researcher. All the verbal solutions and the interpreted notations of each child were videotaped and qualitatively analyzed. Results point out to: forms of additive and subtractive oral calculations, with their corresponding notations (drawings and digits); qualitative comparisons of intensive measures, and additive calculations of basic proportional relations. The support provided to the children by the produced notations was predominant to their verbalization of the calculations and the elaborated relations. The discussion focuses on the relevance of: children's stories as a favorable context to mathematical elaboration of preschoolers, and as a way to integrate the mathematical initiation to the enhancing of children's vocabulary and imagination; forms of teacher's intervention.
children's stories; preschool mathematics; mathematical initiation and children's stories; first arithmetical concepts